How should the presenter handle the transition between slides within the handout? Repeatedly instructing the audience to turn to the next page feels a little 'clunky'.

One way to solve this is to vary your language. Some times you'll say "turn to the next page"; other times "on page 3 we will see how… etc." Keep in mind that with conference room style presentations, you end up with far fewer slides than with ballroom style: typically between 3 and 6, and occasionally even 2 or just 1 outstanding slide. So your audience won't be turning the page very often.

An even better approach is to design your presentation storyline using the S.Co.R.E. approach (Situation, Complication, Resolution, Example). I describe this method in detail in Advanced Presentations by Design, and there is a brief summary of it in step six of the new Design a Presentation feature of the Extreme Presentation website.

(S.Co.R.E. card example from Advanced Presentations by Design)

The benefit of this approach is that you will usually be transitioning on a complication. You’ll be building up your audience’s interest right at the page turn, so that they are curious to see what comes next. For example, you might say: “You probably think that our staff will see this program as just another "flavor of the month." Let me show you why this will not be the case, on the next page, page 3.”

I would like to add that the SCoRE method, as you put it, plays very well with andragogy – adult learning theory developed by people like Malcolm Knowles.
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That “tango”, that dance between Complication/Resolution makes much more sense to an adult, than the pedagogic ideas devised to apply in school, where people without life experience (pupils) are expected to listen to the teacher (someone with life experience and in a position of authority) and consider everything he says as truth.
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In adult education both have life experiences, and both have mental models to help them live and deal with reality. Complication cards come and shatter the prevailing mental model and open space for the opportunity to ear and analyse the new (something related to the “disrupt then reframe technique” that you mention on page 64 of the book).

Andrew,
Just a quick note to thank you for taking the time to answer my question.
The structure you describe (SCoRE) really does seem to lend itself well to transitioning seamlessly between pages. From my understanding of what you describe, the “story” that one is telling would naturally drive the language that one uses to transition between pages, preventing it from becoming repetitive.
Once again, thanks.